Problem with BC-3S10 or Battery?

I am new to the sport of RC aircraft and to RC as a whole. This is my first experience with Li-Po Batteries and chargers. I haven't had my plane for very long and it is a RTF model that comes with a charger and a battery. The charger is a BC-3S10. I have had no issues with it till the other day. Here is how it played out.

I was going to take my plane out and my brothers smaller plate to fly. So I decided to charge the batteries. I charged mine first on my charger. It is a 3S battery so it uses the larger charging port. After mine was done I used my charger to charge his battery which is a 2S so it uses the smaller port. Everything worked fine and both batteries were charged. I had a very successful evening of flying so I decided to get a couple of extra batteries for my plane. When I got them i plugged one it to charge on my charger and it immediately started flashing fast indicating a issue with charging. Thinking my new battery could have a issue i decided to put my old battery that came with the plane on it. I got the same result. LED flashing quickly indicating abnormal charging condition. At that point I decided I may have an issue with the charger. Mostly because I felt it was highly unlikely that all three of the batteries I had would all be bad at the same time. After looking things over and trying to figure out what was going on i decided to try my brothers smaller battery again. I hooked it up and it started charging fine. So now I am not sure what I have going on. Is there any way I can check my batteries to make sure I don't have some issue with them? And if everything is ok there should I just assume I have a charger issue and get a new one?

You can check the batteries with a DVM for voltage.
Fully charged is 4.2 volts per cell. Most inexpensive DVMs are under $20, and read 4.2v as 4.20v +/- about .02v
A 12v light bulb can be used to test the load capability of the battery if you know what the battery current ratings are, and can find an appropriate 12v light bulb and socket.
If you do this, use the DVM to make sure that you do not discharge the battery below about 3.7v-3.8v per cell. This is the storage level for the majority of lipo batteries.

I noticed that others had simiar problems with the BC 3S10 in the past.

Please get rid of that charger. You need a charger that will report the pack voltage, individual cell voltage charging current and milliamp hours returned to the pack during charge. Here are a couple of suggestions.

As Glen indicated those chargers like the one you have are usually just asking for trouble. Very unreliable and don't give you much feed back. Given that a 50W charger can be purchased for around $25 there's no excuse to keep using crap.

As for your problem what's actually in there is basically 3 independent charging circuits, one for each cell of the battery. You said your 3s won't charge but your brothers 2s will. Problem simply is the 3rd charging circuit which is used on cell 3 is bad. Dispose of the charger and get something else.

Since you didn't put your location in your profile it's hard for us to make recommendations on where to buy from. The links to HobbyKing provided are for their international warehouse. If you are in the USA you would want to order from their USA warehouse.